查询词典 one dimensional differential equation

For overcome nonlinear terms of any degree in the equation, we made a proper transformation according to the structure of the equation at first, make the equations into ordinary differential equation. Then solve the ordinary differential equation exactly, by auxiliary functions method and undetermined the coefficient method and algebraic computer system Mathematica.

为了克服方程中非线性项的任意次幂，我们采用的方法是首先根据方程的特点，做适当的变换，使原问题转化为常微分方程的问题，其次对该常微分方程再进行各类变换，如辅助函数法以及待定系数法……。

In the numericalstudy, three-dimensional elastodynamics equations and Morison equation are applied tosimulate the time histories of dynamic response of submarine pipelines suspended over flatbeds sucessfully. The three-dimensional interaction of pipeline and internal flow isnumerically simulated by applying the iterative computation to the fluid-structure interfacesand using the elastodynamic equation and the incompressible fluid N-S equation andcontinuity equation.

在数值研究方面，本文利用三维弹性动力学方程，结合莫里森方程，较好地模拟了规则波浪作用下近壁悬跨弹性海底管线动力响应过程，结合不可压缩流体N-S方程和连续方程，进行管线及其内部流体的三维流固耦合数值计算，基于数值计算结果探讨内流管线系统的动力特性和管内流体特征。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

First the three-dimensional Hailmuhz equation of magnetotelluric field is split into two 2D equations which could be changed into 1D equation by Fourier transformation method. The two zootomic coefficients of the equation are found out by the derivation of vertical component of electromagnetic field being sufficient the equation and the boundary condition. The resolution of 1D equation can be confirmed.

首先将大地电磁场满足的三维亥姆霍兹方程降维分裂成两个二维响应方程，然后对每一个二维方程进行傅里叶变换，使二维方程变为一维方程，通过大地电磁场垂向方向的导数在地面上所满足的边界条件，确定外推方程中的两个待定系数，从而得到一维外推方程的解。

Bosson--One In A Million You're one in a million, Oh now You're one in a million, Oh Sometimes I can't hate you every day Sometimes you can fall for everyone you see Only one can really make me stay A sign from the sky Said to me You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us I've been looking for that special one And I've been searching for someone to give my love And when I thought that all the hope was gone You smile, there you were and I was gone I always will remember how I felt that day A feeling indescribable to me, Yeah I always knew there was an answer for my prayer And you, you're the one for me You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us I was cool and everything was possible You tried to catch me but it wasn't possible No one could hurt me it was my game Until I met you baby and went insane And when you didn't want me, I wanted you Because the finer thing bout it was I like to go I like it when its difficult I like it when it's hard You know it's worth it if ya find your heart You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million You're once in a lifetime You made me discover one of the stars above us You're one in a million, Oh You're one in a million

Bosson--一在A百万 You现在是一个在百万，哦 You是一个在百万，哦 Sometimes我不可能每天恨您 Sometimes您能为您看的每个人跌倒Only一可能真正地做我逗留从天空的A标志对我的Said You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 I寻找那特别一个我搜寻某人给我的爱的AndAnd，当我认为所有希望是去的 You微笑，那里您是，并且我去 I永远将记住我怎么感觉那天感到的A难以描述对我，呀 I总是知道有我的祷告的一个答复And您，您是那个我的 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 I是凉快的，并且一切是可能的 You设法捉住我，但是它不是可能的没人可能伤害我它是我的比赛 Until我遇见了您婴孩并且去疯狂 And，当您没有想要我，我想要您 Because越美好的事回合它是我喜欢去 I喜欢，当它困难我喜欢时，当它是坚硬时You知道它值得它，如果ya发现您的心脏 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万 You一次在一生 You使我发现其中一个在我们之上的星 You是一个在百万，哦 You是一个在百万

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

The equation for item level from item slot is a logarithmic equation and the equation from item level to weapon DPS would require an exponential equation, therefore an equation from item slot value, the value prior to item level, to weapon DPS would be a linear equation.

武器DPS是物品等级中一个很有趣的属性，因为它似乎有多种计算方法。最近加入的传家宝物品可以提出和回答这个问题。物品等级在57以前的时候，它的计算方法和蓝装的线形公式一样，传家宝武器不是线形增长的，似乎是介于线形和多项式增长之间。在58-67的时候，传家宝武器的DPS随物品等级成指数增长。在68-80的时候，武器DPS也是成指数增长，但是速度不同。在100-226之间的史诗物品成相同的指数增长。

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

Limited slip differential is improved according to common differential. Not having the common differentials disadvantage of dividing the torque into two equal parts, limited slip differential can give most torque or even all torque to another driving wheel which is not revolving in order to make use of the friction of this driving wheel to produce enough traction. This will greatly increase the dynamical capability, the passing capability, the stability and the safety of automobiles on different friction roads. So limited slip differential is substitute for common differential.

防滑差速器是对普通差速器的革新与改进，它克服了普通差速器只能平均分配扭矩的缺点，可以使大部分甚至全部扭矩传给另外一个不滑转的驱动轮，以充分利用这一驱动轮的附着力而产生足够的牵引力，大大提高了汽车在双附着系数路面上的动力性和通过性，显著改善了汽车操纵稳定性，有效地提高了汽车行驶安全性，是普通差速器的理想替代产品。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。